We derive a sufficient condition for asymptotic flocking in the Cucker-Smale model with self-delay (also called reaction delay) and with nonsymmetric interaction weights. The condition prescribes smallness of the delay length relative to the decay rate of the inter-agent communication weight. The proof is carried out by a bootstrapping argument combining a decay estimate for the group velocity diameter with a variant of the Gronwall-Halanay inequality.
Haskovec, J. (2022). Flocking in the Cucker-Smale model with self-delay and nonsymmetric interaction weights. Journal of Mathematical Analysis and Applications, 514(1), 126261. https://doi.org/10.1016/j.jmaa.2022.126261